The optical excitation function of prompt Lyman-Alpha radiation, produced by electron impact on atomic hydrogen, has been measured over the extended energy range from threshold to 1.8 keV. Measurements were obtained in a crossed-beams experiment using both magnetically confined and electrostatically focused electrons in collision with atomic hydrogen produced by an intense discharge source. A vacuum-ultraviolet mono- chromator system was used to measure the emitted Lyman-Alpha radiation. The absolute H(1s-2p) electron impact excitation cross section was obtained from the experimental optical excitation function by normalizing to the accepted optical oscillator strength, with corrections for polarization and cascade. Statistical and known systematic uncertainties in our data range from +/- 4% near threshold to +/- 2% at 1.8 keV. Multistate coupling affecting the shape of the excitation function up to 1 keV impact energy is apparent in both the present experimental data and present theoretical results obtained with convergent close- coupling (CCC) theory. This shape function effect leads to an uncertainty in absolute cross sections at the 10% level in the analysis of the experimental data. The derived optimized absolute cross sections are within 7% of the CCC calculations over the 14 eV-1.8 keV range. The present CCC calculations converge on the Bethe- Fano profile for H(1s-2p) excitation at high energy. For this reason agreement with the CCC values to within 3% is achieved in a nonoptimal normalization of the experimental data to the Bethe-Fano profile. The fundamental H(1s-2p) electron impact cross section is thereby determined to an unprecedented accuracy over the 14 eV - 1.8 keV energy range.